> This would seem to be in the same level of complexity as six carrier/modulator interactions; you have to do a multiply to do a lookup after all.

The Yamaha FM synthesis chips do zero multiplications. Everything is done with additions in log scale, with a lookup table for log-sine and another lookup table for exp. I’m unaware of a technique for implementing digital filters without multiplication.

I don’t know why lookup would require a multiplication. Recall that the Yamaha FM chips do not use interpolation.